Self-dual solitons in N=2 supersymmetric Chern-Simons gauge theory

The low energy effective theory of planar QED with a non-local four-fermion interaction including Gross–Neveu and Thirring terms is shown to be equivalent to a Chern–Simons–Higgs model of special characteristics. We study the restrictions imposed by self-duality and supersymmetry, finding in both cases a plethora of (some new) topological and non-topological solitons. The non-relativistic limit of our model generalizes the effective Ginzburg–Landau theory for the fractional quantum Hall effect such that our solitons would be the relativistic version of quasi-particle and quasi-hole excitations.